This week we have something special for our readers.
Whether you’ve seen us in class, in a free event, on this blog, or elsewhere, Kaplan always presents a unified front, as though we agree on everything. In fact, the smart, opinionated people who work for Kaplan disagree about lots of things, and today we’re offering a glimpse of our intellectual disputes.
Kaplan’s GRE bloggers Boris and Teresa take to their chairs to debate a common topic: does a GRE calculator make the test easier, or harder? Hear their arguments, pro and con, in the video below!
As always, let us know what you think in the comments below!
I hear this from a lot of you. Unfortunately, as I explained recently, having more time on the GRE wouldn’t actually help you get a higher score, since the GRE is a scaled test. So let’s leave the complaining to our competition, shall we? Instead of moaning about the clock, strive be as awesome as you can at solving problems. If you’re great, you’ll also be fast. Here’s a quantitative comparison that’s pretty simple, but also a nice illustratration of the fact that speed isn’t something that comes independently of problem solving skill.
This problem, like several I’ve been looking at recently, comes from our GRE Bootcamp event:
Quantity A: The sum of all integers from 9 to 29, inclusive
Quantity B: The sum of all integers from 12 to 30, inclusive
At a glance, the “math” way to solve this problem is time-consuming but direct: add up the sums in both columns, then compare. Since there’s an on-screen calculator on the GRE, some of your competition will solve the problem this way. And boy does it take a long time.
Let me be very clear: directly totaling both columns isn’t just a slow way to solve the problem. It’s a BAD way. Someone who solves the problem in this head-on, brute force fashion, then says to themselves, “I’m fine with the problems, it’s the timing that kills me,” is being dishonest with themselves. They are not ”fine with the problems.” They are very much unfine!
Instead, when you have to compare two quantities, start by eliminating what they have in common. If a quantity appears in both columns, then it isn’t helping either one to be bigger than the other.
Here, both columns include the range of numbers 12-29. Thus, totaling that range would be a waste of time. Ignore it and look instead at what’s different:
Quantity A: The sum of all integers from 9 to 11, inclusive
Quantity B: The of all integers from … never mind, it’s just 30!
And since 9 + 10 + 11 clearly equals 30, you can click choice (C) — “The two quantities are equal” — in under 10 seconds and score the point. That’s the beauty of the GRE: if you’re awesome, speed comes for free. Practice will get you there!
Last year, I wrote a series of entries about the critical reasoning problems that were recently added to the GRE. Since it’s been a while, let’s revisit that question type — and check out another aspect of critical thinking that confounds many of you.
Here’s a type of problem that’s caused no end of consternation to a lot of my students:
Residents of this state are obligated to renew their driver’s license in two circumstances only: if they accumulate six or more points in moving violations, or if they obtain citizenship in another country. Clarice, who is a citizen of only this country, has been involved in only one accident, which added three points to her license. Therefore, Clarice has no reason to renew her driver’s license at this time.
The argument above depends on which of the following assumptions?
I’m not going to show you the answer choices because the essence of this problem needs to be taken care of long before you ever look at a single choice. When I ask my students for the assumption, I invariably hear answers such as the following:
- “The author assumes that Clarice didn’t receive points from sources other than accidents.”
- “The author assumes that Clarice wasn’t already a citizen of some other place.”
- “The author assumes that Clarice didn’t do something else that would make her have to renew her license.”
All of these wrong answers fall for the same trap: thinking in the way that the test makers want you to think. The test makers say, “Hey! Look at these conditions. Clarice didn’t meet any of them. So, there’s no reason for her to renew her license.” And a lot people look at that line of reasoning and say, “Aha! I bet Clarice DID meet one of those conditions, in some sneaky way.” Then they start drumming up clever ways to force poor Clarice to retake her driver’s exam.
This is what I like to call going down the wrong rabbit hole. The test makers show you a rabbit hole, saying basically, “Hey, you! Think about THIS.” And so you think about whatever “this” is, and you think about it really hard, and the problem is that you shouldn’t have even started thinking along those lines in the first place.
Let’s back up a bit.
Consider this argument:
Boris isn’t obligated to exercise. Therefore, there is no reason for Boris to exercise.
Or how about this one:
There is no law mandating that Boris be kind to his mother. Therefore, he should be a jerk to her.
How do those arguments sound? Terrible, you say?! But why? If I’m not required to do something, doesn’t that mean I have no reason to do it?
Here, again, is the argument about Clarice, but condensed to the essentials:
Clarice isn’t required to renew her driver’s license. Therefore, she has no reason to renew her driver’s license.
It’s tricky to spot the error the first time someone throws you an argument like this, because renewing a driver’s license is boring and lame, so your brain fills in the gap in the argument: “The only reason anyone would ever renew their license was if they had to.” But that’s not necessarily true: that’s an assumption. Maybe Clarice gets a tax credit for renewing her license, or renewing the license will get some of her points taken away, or renewing the license provides some other benefit to something completely unrelated. We don’t know.
Remember this nugget of logical wisdom when you take the GRE: just because a person isn’t required to do something, doesn’t mean that they shouldn’t or they won’t!
The chat lit up with excitement. I was expecting a positive response, but there was so much enthusiasm that I was taken aback. One student called it “a blessing.” Many others agreed that if they had 15 extra minutes per section, it would be just about the greatest thing that’s ever happened to them: they’d be less stressed, get more problems right, have a higher score; the sun would shine brighter and longer and warmer; a cavalcade of parachuting puppies would rain down from the sky and deliver every child in the world a cupcake made of love and hope; a cadre of unicorns would …
“HANG ON, HANG ON!” I said. “If you had more time to work on each section … what else would happen?”
And then there was silence. For a moment, the class was confused. Nobody saw what I was getting at. I prodded a little more, and finally one student said, “… other people would have more time too?”
Another student caught on. “And the scoring scale would be harder.”
Right. If you had 15 extra minutes per section, that would be terrible! Your competition would get the same bonus you would, so it’d be exactly as hard to get any particular score as it is now, except the test would be 75 minutes longer. Because every student’s score depends entirely on her performance relative to everyone else, a feature that benefits everyone actually benefits no one.
Don’t rail against the strict time limits of the GRE. Don’t fume, saying, “This is stupid. If I had infinite time, I could get all these questions right!” The thing is, if you had infinite time, so would your competition, and you wouldn’t be any better off. Learn to love the clock — it’s an opportunity for you to succeed where others fail.
Not too long ago, I used something called the “balance approach” to show you how to solve a mixtures problem. But the balance technique isn’t exclusive to mixtures. In fact, the most likely time for it to come up is when a problem deals with plain ol’ averages.
Here’s an example of the kind of GRE problem I’m talking about:
At a bowling tournament in which males and females competed, the average score of the participants was 154 points. If the average score of the 8 males was 148 points, how many females were in the tournament if the average female score was 158 points?
Most of your competition is going to try to use the average formula: average equals sum divided by number, or as I prefer to write it,
Average × Number = Sum
Using the above formula gives you this:
154(8 + x) = 8(148) + x(158)
There are a couple of problems here. One, you have to do some nasty arithmetic, such as 154×8 and 8×148. And perhaps more importantly, it takes a rather impressive feat of translation to set that baby up.
Try this instead.
The overall average is 154. Each man got 148 points, which is 6 points short of the average. There were 8 men, so altogether, they dragged down the average by 8×6 = 48 points.
This means the women need to make up a 48 point deficit. Each woman scores a 158, which is 4 points above the average. If each woman contributes 4 points to overcoming the 48 point shortfall, then there need to be 48/4 = 12 of them.
That sure was a lot easier than solving the equation. And if you’re a real critical thinking wizard, you might notice that even this was too much work. The ratio of the men’s deficit (-6) to the women’s surplus (+4) is 6 to 4, or 1.5. Thus, the ratio of women to men also needs to be 1.5, and that it is: 12÷8 = 1.5.